Geodesic
Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case
Oana Ivanovici1 ; Gilles Lebeau2 ; Fabrice Planchon3
1 CNRS and Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France
2 Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France, and Institut Universitaire de France
3 Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France and Institut Universitaire de France
Annals of mathematics, Tome 180 (2014) no. 1, pp. 323-380.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We consider a model case for a strictly convex domain $\Omega\subset\mathbb{R}^d$ of dimension $d\geq 2$ with smooth boundary $\partial\Omega\neq\emptyset$, and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case, due to repeated occurrences of swallowtail type singularities in the wave front set.
DOI : 10.4007/annals.2014.180.1.7

Oana Ivanovici 1 ; Gilles Lebeau 2 ; Fabrice Planchon 3

1 CNRS and Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France
2 Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France, and Institut Universitaire de France
3 Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France and Institut Universitaire de France 
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     title = {Dispersion for the wave equation inside strictly convex domains {I:} the {Friedlander} model case},
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Oana Ivanovici; Gilles Lebeau; Fabrice Planchon. Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case. Annals of mathematics, Tome 180 (2014) no. 1, pp. 323-380. doi : 10.4007/annals.2014.180.1.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.1.7/

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